qnorm.js

qnorm.js

// Originally found at: http://rangevoting.org/Qnorm.html

/** * @(#)qnorm.js * * Copyright (c) 2000 by Sundar Dorai-Raj
  * * @author Sundar Dorai-Raj
  * * Email: sdoraira@vt.edu
  * * This program is free software; you can redistribute it and/or
  * * modify it under the terms of the GNU General Public License 
  * * as published by the Free Software Foundation; either version 2 
  * * of the License, or (at your option) any later version, 
  * * provided that any use properly credits the author. 
  * * This program is distributed in the hope that it will be useful,
  * * but WITHOUT ANY WARRANTY; without even the implied warranty of
  * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
  * * GNU General Public License for more details at http://www.gnu.org
  * * */
  
var qnorm = function(p) {
  // ALGORITHM AS 111, APPL.STATIST., VOL.26, 118-121, 1977.
  // Computes z = invNorm(p)

  p = parseFloat(p);
  var split = 0.42;

  var a0 = 2.50662823884;
  var a1 = -18.61500062529;
  var a2 = 41.39119773534;
  var a3 = -25.44106049637;
  var b1 = -8.47351093090;
  var b2 = 23.08336743743;
  var b3 = -21.06224101826;
  var b4 =  3.13082909833;
  var c0 = -2.78718931138;
  var c1 = -2.29796479134;
  var c2 =  4.85014127135;
  var c3 =  2.32121276858;
  var d1 =  3.54388924762;
  var d2 =  1.63706781897;

  var q = p - 0.5;

  var r, ppnd;

  if (Math.abs(q) <= split) {
    r = q * q;
    ppnd = q * (((a3*r+a2)*r+a1)*r+a0)/((((b4*r+b3)*r+b2)*r+b1)*r+1);
  } else {
    r = p;
    if (q > 0) r = 1 - p;
    if (r > 0) {
      r = Math.sqrt(-Math.log(r));
      ppnd = (((c3*r+c2)*r+c1)*r+c0)/((d2*r+d1)*r+1);
      if (q < 0) ppnd = -ppnd;
    }
    else {
      ppnd = 0;
    }
  }

  return ppnd;
}